Aerial Photography and Remote Sensing – Study Outline

height by differential parallax

You should be able to:

1. describe what differential parallax is.

2. name and describe how to measure the variables in the differential parallax equation

3. calculate the height of an object using differential parallax

4. describe the importance of control points for accurate air photo measurements

5. describe the difference between an orthophoto and a normal aerial photo

A. Most measurements of height on aerial photos use differential parallax of stereo pairs

1. a stereo pair is formed whenever two photos have some image overlap

a. to view a stereo pair the images must be placed so that the overlapping parts are together in the middle and the parts of the image that are not shared are on the outside

b. the flight lines must line up on the two photos

2. differential parallax --

a. on a single photo the amount of displacement increases with distance from the center

b. on a stereo pair the displacement of any object is different on each photo because the center of the photo moves between the images

i. you eye uses this difference to create the 3-D image

c. although the total displacement is different for every object, the amount that the displacement changes from one photo to the next is exactly the same for a given height everywhere in the overlapping images, this change in displacement is the differential parallax

i. the differential parallax increases with height above the base level

ii. the differential parallax increases the farther the plane moves between photos

d. the height of an object can be calculated from the formula h = H * dP / (P + dP)

i. H is the height of the camera above the reference height

ii. P is the photo baseline – the distance the plane moved between photos

- P is calculated by first finding the center of each photo (the principle point) and the location of the center of the other photo on each photo (the conjugate principle point)

- P is distance between these points (on level ground it should be the same)

- for accuracy, it is best to measure on both photos and take the average.

- the line between these points indicates the flight line of the airplane.

iii. dP is the differential parallax, how much more one part of an image moves toward or away from the center of the photo parallel to the flight line relative to another

- dP is measured by lining up the photos for stereo viewing, making sure that the flight lines are aligned.

- subtract the distance between the images of the base level or reference point on each photo from the distance between the images of the point you are measuring

(i) if the point you are measuring is above the base the distance will be smaller and dP is positive

(ii) if the point you are measuring is below the base, dP will be negative.

iv. points to remember

- dP and P are in the same units, and are measurements on the photo

- h will be in the same units as H, which are real world measurements and will be in different units than P and dP

- in very hilly terrain this equation will give an approximate result, but the exact formula is a bit more complicated

3. control points

a. accurate measurements of distance and height require at least three points on each photo with known position and elevation for all control points

b. for hand measurements control points allow calculation of the scale and flying height.

c. with special equipment or software, control points allow for correction of lens distortion and tilt as well.

4. orthophotos

a. an orthophoto is an aerial photography in which high points have been digitally or mechanically squeezed and and low points stretched to remove the displacement of vertical parallax

b. the advantages of orthophoto are

i. the entire photo has a single scale even in hilly terrain

ii. the photo can be used like a map for accurate measurement of distances, angles and areas

c. the disadvantages of orthophotos are

i. stereo viewing is no longer possible (unless a special othostereo pair is created)

ii. the process of correcting the image reduces the resolution